[MUSIC] The faucet has a slow leak. It's dripping.
How much water is being wasted? Let's find out.
Now, I'm going to start the timer and see how full the measuring cup is after, say,
three minutes. [MUSIC] So, after three minutes of
dripping, the drip has put approximately 13 milliliters of water into this
measuring cup. Here, I have a cube that holds one liter
of liquid. How long would it take our dripping
faucet that drips 13 milliliters per three minutes to fill this cube that
holds 1000 milliliters? [MUSIC] Alright.
It's been about 90 minutes. Let's see where we're at.
It looks like almost exactly 400 milliliters.
So, we've collected some data and now, let's see if we can figure something out.
Alright. Here at time and time and water.
After three minutes, we found that 13 milliliters of water are inside the
measuring cup. This tells us that the water is entering
the measuring cup at a rate of 13 milliliters for three minutes, which is
equal to or approximately [SOUND] 4.3 milliliters per minute.
Later, we checked it and we found that after 90 minutes, there were 400
milliliters in the cube this time. Well, this tells us since going from here
to here, we have a difference of 87 minutes and going from here to here, we
have a difference of 387 milliliters, this gives us a new rate.
It says, that we have 387 milliliters per 87 minutes and that's approximately 4.4
milliliters per minute. Aha.
This looks like it's linear growth. I know that the slopes are slightly
different but such a, such a small difference that if we plot it, it should
be linear. Now, at what time is there one liter of
water in the cube? That would be 1,000 [SOUND] milliliters.
At what time? So, we should use t for the variable
there. We have to solve the following equation.
We want 1000 / t to be approximately well, what's between 4.3 and 4.4?
4.35, okay? Ha, ha.
So now, that's the same as saying, t is equal to 1,000 / 4.35 five, this is
approximately 230 minutes. 230 minutes is 3 hours, 50 minutes.
[MUSIC]
At this point, 3 hours and 50 minutes has gone by.
If we check the cube, [MUSIC] we see it's right at a 1,000 milliliters.
[MUSIC]